%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET891+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 15:33:39 EDT 2023

% Result   : Theorem 0.11s 0.29s
% Output   : Proof 0.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SET891+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.08  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.26  % Computer : n032.cluster.edu
% 0.09/0.26  % Model    : x86_64 x86_64
% 0.09/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26  % Memory   : 8042.1875MB
% 0.09/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.26  % CPULimit : 300
% 0.09/0.26  % WCLimit  : 300
% 0.09/0.26  % DateTime : Sat Aug 26 12:58:29 EDT 2023
% 0.09/0.26  % CPUTime  : 
% 0.11/0.29  Command-line arguments: --no-flatten-goal
% 0.11/0.29  
% 0.11/0.29  % SZS status Theorem
% 0.11/0.29  
% 0.11/0.29  % SZS output start Proof
% 0.11/0.29  Take the following subset of the input axioms:
% 0.11/0.29    fof(l52_zfmisc_1, axiom, ![A, B]: union(unordered_pair(A, B))=set_union2(A, B)).
% 0.11/0.29    fof(t32_zfmisc_1, conjecture, ![A2, B2]: union(unordered_pair(singleton(A2), singleton(B2)))=unordered_pair(A2, B2)).
% 0.11/0.29    fof(t41_enumset1, axiom, ![A2, B2]: unordered_pair(A2, B2)=set_union2(singleton(A2), singleton(B2))).
% 0.11/0.29  
% 0.11/0.29  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.11/0.29  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.11/0.29  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.11/0.29    fresh(y, y, x1...xn) = u
% 0.11/0.29    C => fresh(s, t, x1...xn) = v
% 0.11/0.29  where fresh is a fresh function symbol and x1..xn are the free
% 0.11/0.29  variables of u and v.
% 0.11/0.29  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.11/0.29  input problem has no model of domain size 1).
% 0.11/0.29  
% 0.11/0.29  The encoding turns the above axioms into the following unit equations and goals:
% 0.11/0.29  
% 0.11/0.29  Axiom 1 (l52_zfmisc_1): union(unordered_pair(X, Y)) = set_union2(X, Y).
% 0.11/0.29  Axiom 2 (t41_enumset1): unordered_pair(X, Y) = set_union2(singleton(X), singleton(Y)).
% 0.11/0.29  
% 0.11/0.29  Goal 1 (t32_zfmisc_1): union(unordered_pair(singleton(a), singleton(b))) = unordered_pair(a, b).
% 0.11/0.29  Proof:
% 0.11/0.29    union(unordered_pair(singleton(a), singleton(b)))
% 0.11/0.29  = { by axiom 1 (l52_zfmisc_1) }
% 0.11/0.29    set_union2(singleton(a), singleton(b))
% 0.11/0.29  = { by axiom 2 (t41_enumset1) R->L }
% 0.11/0.29    unordered_pair(a, b)
% 0.11/0.29  % SZS output end Proof
% 0.11/0.29  
% 0.11/0.29  RESULT: Theorem (the conjecture is true).
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